IMO - assuming you are talking about a heavy rifle - it really comes down to personal choice and what you will be using the gun for. As a professional back-up gun for dangerous game, ejectors would be optimal for most, so long as you are used to ejectors and practice with it a lot. But that is the only situation where I think you would NEED ejectors in any way (for speed on reload), aside from that it is really just preference and getting experience with that gun (whatever it be). for an extractor-only gun there are different methods for shooting it and reloading fast.

Picking up brass, yeah for sure ... but with an extractor gun if you pull the brass out by hand you still have the problem of having two empty shells in your hand OR you rolled the gun over and the shells fell on the ground anyway!! Double rifles are great in that you can shoot 4 - 6 - 8 shots very fast - so it is all about the reloading function to me.... otherwise extractor/ejector, wouldnt make a difference.

Pretty soon I will have both a heavy extractor DR AND a heavy ejector DR - and that will present a new set of issues for me... getting used to shooting both types!!! A lot of that would come down to setting in place processes where you (or me) mentally check and recheck when you go to shoot the gun - and that is a good way to practice with any firearm in the field or at the range.... if you know what I mean?

Work out how YOU are going to operate the firearm and drill that operation, often, with mental checks...